Here's what we do. When we are creating a new site, we use responsive design... but we also create a separate mobile version that looks and behaves like an app store app, but it's actually just a jquery/css web app.
When the user visits the site on a smartphone, they are redirected to the web app. We include a link to the full site that is enabled using cookies so that if they click on "View the full Site", they are taken to the responsive design site.
This serves two functions, first, the important info - call us, find us, email us, learn about us and other site specific info is served up right away. This is essential for most brick and mortar businesses. The second function is that if the user for some reason needs more info, they can get it directly from the responsive full site.